Archive for April, 2007

Awhile back I spent a bunch of posts (start here if you want to read them) discussing an academic paper by economists Cade Massey and Richard Thaler. One of their findings that I didn't talk much about --- largely because I didn't have any explanation for it myself --- is the high discount rate on future draft picks. From their paper:

A third notable feature of these data is the remarkably high discount rate, which we estimate to be 174% per year.

...

We suspect that one reason why the discount rate is high is that picks for the following year have additional uncertainty attached to them since the exact value depends on the performance of the team trading away the pick in the following year. Still, this factor alone cannot explain a discount rate of this magnitude. Clearly teams giving up second-round picks next year for a third-round pick this year are displaying highly impatient behavior, but it is not possible to say whether this behavior reflects the preferences of the owners or the employees (general manger and coach) who make the choices (or both).

In other words, your round N pick this year for my round N-1 pick next year (which is the standard rule of thumb) is not a good deal for me unless I place a massive premium on winning now as opposed to winning later. Or, as Massey and Thaler put it, unless I'm highly impatient. This is indeed puzzling, but I think I may have an explanation, and it came to me while sifting through the discussion of the Brady Quinn trade.

Dallas gave up #22, which is worth 780 points according to the pick value chart, while Cleveland gave #36 (worth 540) plus their first round pick in 2008. You can run the numbers with various assumptions, but for the sake of definiteness let's just assume that the Browns' pick will be #8 overall selection next year. The #8 pick, according to the chart, is worth 1400 points. So according to the chart, Cleveland is willing to give up 1400 points next year for a gain of only 240 points this year. Highly impatient indeed.

But wait. Cleveland wasn't giving up 540 points this year and 1400 points next year for "the #22 pick." They were giving up 540 points this year and 1400 points next year for Brady Quinn, which is a very different thing. Cleveland obviously values Quinn more highly than an average #22 pick, which is why they made the trade. They wouldn't have dreamed of making that deal three hours prior.

If Cleveland thinks Quinn is as good as an average #3 or #4 overall pick (roughly 1800 points), an idea which wouldn't have raised too many eyebrows on Saturday morning, then the Browns are not paying any interest at all. They're earning interest!

Even if they didn't value Quinn quite that highly, say they think he's worth a typical #6 or #7 pick (which again would not have seemed remotely controversial a few days ago), then it looks like this: Cleveland immediately acquires a commodity that they think is worth about 1600 points. To do this, they give up 540 points right now, and somewhere around 1400 points next year. There is a discount rate, as there should be, but it's not 174%.

And this is typical. Teams that give up future-year picks are always the teams that are trading up. And teams generally trade up only when they are targeting a particular player, like Quinn, because they value him more highly than they'd value a generic player in that slot.

Let's look at some other trades from Saturday involving future picks:

The Colts traded their #1 pick in 2008 (let's say 600--700 points), along with pick #126 (worth 46 points), to San Francisco for pick #42, which the Colts used to select Tony Ugoh. If the Colts view Ugoh as being as good as a typical late first round pick, again a not-totally-wacky notion, then there is no discount rate at all.

Similarly, San Diego moved up to grab Utah safety Eric Weddle at #37, giving up their 2008 third-rounder, among other things, in the process. If you add in the 2008 pick at full value, they gave up 587 points for him, which is about what pick #32 or #33 is worth on the chart. Again, some analysts had Weddle ranked in that general vicinity.

So I think Massey and Thaler were sort of right, or exactly wrong, depending on how you look at it. The apparently-high discount rate comes about not because of uncertainty about next year's pick but because of complete certainty about this year's pick. Cleveland was not overvaluing this year's #22 pick relative to next year's #8 (or whatever) pick. Cleveland, in fact, didn't make a trade for this year's #22 pick. They made a trade for Brady Quinn.

The Browns' front office might indeed be guilty of falling into another of the psychological traps mentioned by Massey and Thaler: overestimating their own ability to judge Brady Quinn as a prospect. But I don't see any reason to believe that they were acting impatiently.

[First, a final reminder to enter the p-f-r draft contest. Entries must be time stamped before a pick is made.]

When I started this blog, I wanted it to be unique; I wanted it to be a place where you could read something different from what's being printed elsewhere. On the eve of the draft, I have opinions on Calvin Johnson and Adrian Peterson and Amobi Okoye, but it's not worth my time or yours for me to write them down. They simply don't add anything to the discussion. But the media frenzy surrounding the NFL draft and the absence of anything else football-related to talk about for the past two months leave me in a rough spot. If I want to say something that hasn't yet been said, it's going to have to be a little bit crazy. So I'm opening up a new category: Insane ideas. The ideas posted in this category are not meant to be taken too seriously --- I'm labeling them insane, after all. So I recognize that ultimately most of them will probably not be good ideas, but I am not just blatantly trolling either. I do believe there may be a kernel of a good idea in these posts.

So here goes with insane idea #1. Bear with me while I set it up...

Let's say you're in a football stadium with 80,000 of your closest friends watching a big game. For much of the time, you and your 80,000 friends are content to sit down, because it's more comfortable than standing up. But when something exciting starts to unfold, people start to stand up. Maybe for awhile, you can remain comfortably seated and still see the action. But as soon as some guy in front of you stands up, you have to stand up to have any chance of seeing over him. This, of course, forces the people behind you to stand up, which forces the people behind them to stand up, and so on. Pretty soon, everyone is standing.

But now everyone is worse off than they would have been if they all had simply remained seated. Any particular individual can gain a better view by standing up, which is (one reason) why people do it, but if everyone stands up then no one has a better view. The only difference is that everyone is now less comfortable.

This is not a novel observation. But let's take it a bit further. It's not quite true that everyone has the same view standing up as they do sitting down. The difference between tall people and short people gets magnified when people stand up. To put it another way, sitting is something of an equalizer. If the guy in front of me is taller than I am, then I might be able to see over him when we're sitting, but I can no longer see over him when we're standing. So if I'm short, a logical response might be for me to simply opt out of the standing up game completely. When everyone else stands up, I'll just stay seated. Sure, I'd like to watch the live action, but I'm simply too short to see over the guy in front of me. Standing up doesn't do me any good. Next game, I'll bring a stepstool to stand on. Or maybe I'll bring a little pocket TV. Or maybe I'll just stay home and watch the game on TV. That's not quite as enjoyable as live action, but I wasn't getting all the benefits of the live action anyway, and I was paying a lot of money for the privilege. If I don't buy season tickets, I could afford, for example, a much nicer car.

OK, at this point what we've established nothing more than that I am probably the most annoying and overly analytical football game companion imaginable and that you should not offer me a spare ticket if you happen to have one. But I'm setting up an analogy, and here it is:

If every team did its scouting using Street & Smith's college football preview magazine and watching a few college football games a week (as I understand was essentially the case when the draft was young), things would be easy for everyone and everyone would be basically in the same boat. But then Gil Brandt and his obnoxious Cowboy cronies started to stand up. They beat the bushes looking for small college players. They started conducting interviews and actually try to get to know the players. Now they can see the game pretty clearly, and that puts me and my Street & Smith's at a disadvantage. So I'd better stand up too. Pretty soon everyone is standing up and for the most part everyone is in the same boat again, except that we're all spending an obscene amount of time and money.

But we're not quite in the same boat. Some teams (if you're following along, these are the short people) are spending an obscene amount of money and still not seeing the game. What options do they have? Well, they can either buy a stepstool, or they can stay home and watch the game on TV. In this scenario, buying a stepstool corresponds to pouring a lot more resources into your scouting department: hiring more people and/or better people and giving them a bigger budget. But this kind of stepstool is expensive and it comes with no guarantees. It might collapse the first time you try to hoist your short self up onto it.

I'm more interested in the other option: watching the game on TV. I.e., settling for a slightly less appealing but much less expensive alternative, and then using the excess money to improve my life in some other way. What does this correspond to in the analogy? Is there a slightly less appealing but much less expensive alternative to spending resources scouting prospects?

I'd like to suggest that at this point the amount of freely-available information about the draft is so mountainous that, if you believe there is wisdom in crowds, it's not completely insane to believe that compiling all this public information in an intelligent way could constitute a reasonable substitute for a scouting department. In other words, the internet and a bunch of draft publications (maybe even Street & Smith's!) might be your TV.

I am not saying that teams who utilize this plan would typically have good drafts. But is it so hard to believe that you could, in the long run, have a drafting record that is only slightly below average with this plan? I am certainly not saying that your 19-year-old cousin who set up a draft website in his parents' basement is as good at evaluating talent as professional NFL scouts are. Rather, I am suggesting that, if he's a smart kid, he can learn a whole lot by piggybacking on the enormous body of work that is being done and reported on by professional scouts and others. There are a lot of sharp football minds, including some former professional scouts, who break down gobs of game film, who go to the college all star games and all the other events, who talk to the players, who talk to agents and NFL personnel men, and whose full time job is to provide information about draft-eligible college football players to anyone who wants to pay a small fee for it. There is also probably a lot of information to be inferred from reading factual accounts of which front offices were present at which pro days, which prospects were making visits to which teams, and so on.

If I paid Chase $50,000 per year to spend his every waking hour unearthing every possible nugget of information he could get his hands on, and finally synthesizing it into a draft board, could it pass for the draft board of a real NFL team? Having never seen one of the latter, I can't say. But seriously, how much worse could the result be than the drafts the Detroit Lions have had during the last decade? Or the Browns? In addition, I could employ a Massey-Thaler-like strategy of trading my high picks for multiple middle round picks, thereby minimizing my exposure to a single piece of bad information that Chase might have missed because he's not a real scout.

Now I know what you're thinking: concocting a plan to produce drafts better than the Lions of the late 90s and early 00s isn't exactly going to pave the road to the Super Bowl, which should be my ultimate goal. You're absolutely right. But remember the short guy who decided to watch the games on TV even though he'd have preferred to watch in person. Making that change wasn't necessarily a net loss of overall happiness for our short friend because, if you'll recall, he used his season ticket money to upgrade his next new car purchase from a Kia to a Honda.

And that's the crux of the matter. It's all fine and well to save millions (tens of millions?) on scouting every year, if I can find some other way to spend that money that will help my football team more than my cheap scouting budget will hurt it. With a salary cap in place, I can't spend the extra money on veteran players, but there may be other options. Maybe I could upgrade my next coaching hire from Wade K. Phillips to Bill H. Cowher. Maybe I could hire the absolute best offensive and defensive coordinators in the league and pay them enough so that they wouldn't be tempted to flee for a head coaching job. Maybe I could upgrade my facilities to make my team a more attractive destination for free agents. Maybe a bigger and/or better staff of team doctors and trainers (or groundskeepers) would help me keep my team healthier than average in the long run. We're talking about a lot of money saved here.

Like just about everything in life, winning football games is about the allocation of resources. Every team has a budget and must decide how to divvy it up among the various enterprises that comprise the final product. Most of the time, spending extra resources to improve one aspect of the team means that some other aspect will have to make due with less.

Now that doesn't mean that you can just spend your resources any old way and get the same result. For example, I would not as a general policy recommend saving 6 million dollars per year by always fielding a starting quarterback who is willing to play for the league minimum. Why not? Because the dropoff in production would probably be so steep that you'd be hard pressed to make it up by spending that money elsewhere. The difference here is that I'm (sort of) confident that a huge drop in expenditures in the scouting department might only lead to a small drop in production. If that's the case, then it's likely that the production drop can be more than recouped with a huge expenditure in some other area.

As promised, this idea is insane. But also as promised, I think there is a good idea at the core of it: skimp on scouting. Not because scouting isn't important; it's very important. But why foot the bill, when others (including your competitors!) are willing to do a lot of the work for you? If your scouting department has been doing a below average job, I'm about 95% sure that Chase could do almost as good a job for less than 1% of the salary. What I'm less sure of is whether or not I could find a way to use the savings productively.

About this time last year, I posted a list of all 32 teams along with an estimate of the net effect of their player movement during the offseason.

The intro to that post will serve as a good one for this post too:

Most of the free agency dust has settled by now. If you’ve lost track of who’s where, check out this handy dandy player movement tracker at my other site, footballguys.com. You can sort and sift the list based on a number of different criteria to get a feel for this offseason’s activity.

The tracker has a column labeled “Importance” that ranks each player on a scale of one to five. Nate Clements is a five. Sean Morey is a one. Tatum Bell is a three. These numbers are not scientifically determined and should only be used to place players into large buckets. Nonetheless, I couldn’t help running with an idea suggested by a footballguys message board poster named “Kleck.”

He suggested that we add up, for each team, the total “Importance” of the players acquired minus the total Importance of the players departing. This will give us an imprecise-but-generally-somewhat-reasonable measure of which teams have improved and which teams have declined. Here is the list, sorted from most improved to most declined:

And so here it is for 2007. If you mouse over a team, you can see the players of importance three or greater who were gained and lost.

For what it's worth, last year's list had the Texans and Lions as the biggest gainers, and the Patriots, Colts, and Chargers as the teams suffering the greatest net free agent losses. Since those latter three were arguably the three best teams in the NFL last season, it's pretty clear that not too much should be read into this, but it's interesting to look at anyway.

On the NFL Network's draft preview show earlier this week, Mike Mayock expressed frustration that more and more prospects --- all of them, basically --- are spending January through March training specifically for combine drills. This makes it difficult to determine whether those 40 times represent real speed that will translate to the football field, or merely track speed that will disappear as soon as the pads go on and the players are having to think and run at the same time.

As a college professor who occasionally participates in admissions-related activities, I can sympathize. Just as the skills (namely speed, quickness, and strength) that lead to good results in combine drills are closely related to the skills that players need to succeed in the NFL, the skills that cause a student to do well on the SAT are indeed correlated with the skills that cause students to succeed in college. But what a student learns at an SAT prep class serves only to improve the test score itself, not to improve the actual abilities that admissions people hope the test is trying to measure. One test prep center advertises, "Spend a little time getting to know the SAT better and you can find out how to use the structure and format of the test to your advantage." In other words, it's not about making yourself more prepared for college. It's about making yourself appear more prepared for college.

If I had access to an honest account of how many hours of SAT prep each applicant had (and in which program), I think I could make smarter admissions decisions by discounting the scores of those who spent the most effort bolstering their appearance.

I, of course, have no such account. But NFL teams do. They know exactly where all these players have been spending their time since January. So this seems to me like an opportunity for smart teams to gain an advantage. Some of these combine training facilities have been around for a decade now. Figure out how many hundredths each of these camps shaves off the 40 time of a typical player. Then figure out whether those hundredths stayed off when the player reached the NFL. In other words, did they teach him how to run a faster 40, or did they actually teach him some meaningful techniques that he was able to translate to the field? If the former, and then add it back on for the purposes of evaluation.

Suppose a guy "played like a 4.6 guy" in college, but ran a 4.45 at the combine. Go look at his rookie year film and determine whether he played more like a 4.6 guy or a 4.45 guy in the pros. You might find that the guys who worked out at Training Facility A were in general able to maintain their speed gains while those who trained at Facility B were not.

Don't be frustrated by it, use it.

On the flip side, if I were an agent, I might at this point be tempted to hire a team of ex-NFL coaches and publicly advertise that my players are specifically not training for the combine drills. Instead, they're getting actual NFL coaching, doing football work, and learning how to train like NFL players train. Essentially, my guys will have a head start in terms of picking up NFL terminology and schemes because they haven't been wasting their time learning to keep their elbows in while they run, or trying to put on weigh-in pounds that are going to come off after three days of real practice.

Last week I posted some summary data on how teams have historically used their first round selections. I decided to expand that to the entire draft while accounting for the fact that the picks at the top of the draft are in general more valuable than those at the end.

So I took the pick value chart value of each draft pick by each team since 1978. Then I computed the percentage of each team's total pick value that it used on each position.

For example, the Texans have drafted five wide receivers in their history: Andre Johnson (#3, value 2200), Jabar Gaffney (#33, value 580), Jerome Mathis (#114, value 66), Sloan Thomas (#211, value 7), and David Anderson (#251, value 0). That's a total of 2853 "value points" spent on the wide receiver position. In their five year history, they have had a total of 15730 points to work with, so they've spent 18.1% of it on wide outs.

Below is a table showing every team's percentage of draft value spent on each position since 1978.

How crazy would it be to infer that these represent what the league as a whole believes the relative importance of the positions to be? Probably a little crazy, but maybe only a little. Even if you think the draft value chart is out of whack, it is supposed to be what the teams have developed as a de facto standard of value, right? Each team has a limited number of "value points" to spend each year, and they should in the long run allocate those points in roughly the same proportion as the relative importance of the positions.

Quarterbacks account for 7.4% of the draft expenditures and 4.5% of the players on the field at any given time. Does this mean that a quarterback is on average about 64% more important (whatever that might mean) than an average player?

It gets a little less clear when you try to look at, say, wide receivers. They account for 11.7% of draft expenditures. But if I want to know how important an average wide receiver is, am I supposed to divide that by two, or three, or 2.5, or six, or what?

It is interesting that at almost all times, there are more defensive backs on the field than defensive linemen, yet more draft capital has been spent on linemen. Likewise, more draft capital has been spent on defensive linemen than on offensive linemen, despite the fact that more offensive linemen are on the field at all times.

One final tidbit for discussion. Here is the same table, but only considering 1998--2006:

2. A p-f-r user named Steve pointed out an error at the site, which I corrected this weekend. In particular, the offensive team passing yard totals didn't match the defensive team passing totals for 2004, 2005, and 2006. I was showing net passing yards on the defensive side, and gross passing yards on the offensive side. Both sides now show gross yards. That is, sack yardage is not included. [As an aside, why in the world do I not include sack yardage, anyway? It's a long story that's not worth the time to tell because I'm about 99% sure that I will be including sack yardage on the team pages in the very near future.]

It's much easier to implement. Not only does it not require javascript, it doesn't even require css.

The text does not pop up immediately; it only does so if you hover the mouse for a couple of beats. In the comments of the previous post, Vince remarked, "I hate websites that throw info/sounds/pics up at me when I did not request them." I definitely understand where he's coming from. But I wonder if this doesn't satisfy even Vince. I would argue that leaving your mouse on a link for at least a second is requesting the information. If you just run the mouse over it on your way to some other link, it doesn't appear at all. What say you, Vince?

With this scheme, no formatting (bold, tables, links, etc) is allowed. It has to be plain text and it has to be one line. I think this will keep me from being tempted to put too much information into a tooltip. If it's enough information to deserve formatting and/or more than one line, then it deserves its own page.

The nominal reason for the draft is to give the worst teams the first shot at the top talent, thereby helping achieve competitive balance in the league. But it obviously doesn't work that way.

If this were the old days, the Raiders could take Calvin Johnson or JaMarcus Russell and pay him nothing, while the Colts would take Ben Grubbs or Brian Leonard and pay him essentially the same nothing. That helps the Raiders.

But this isn't the old days. The Raiders will have to pay whoever they take much more than the Colts will have to pay their pick. Because of the salary cap, that means the Raiders will have less to spend on other players. The recent academic paper by Cade Massey and Richard Thaler (which I've written about here, here, and here) argues that the reality of the situation is that this setup actually hurts the Raiders. I don't think that's quite right, but I agree that it doesn't help the Raiders much if at all.

If the goal of the draft is to help even out the competitive landscape of the league, I don't think it's working. And as long as there is a salary cap, I don't think it's going to work.

That's the nominal reason for the draft. The real reason for the draft, as observed by Jim A in the comments to an old post, is to keep money out of the hands of the rookies and in the hands of the owners and the veterans.

I have no evidence to back this up, but I'm not convinced that's happening. Vince Young signed a deal last year that will be worth between 26 and 58 million dollars. Do you really think he would have gotten much more if he were on the open market? Before you answer yes and cite increased demand, remember that there would be increased supply too: the teams bidding for him would have had the option of bidding on Matt Leinart or Jay Cutler as well.

So the way I see it, the draft isn't doing what it says it's supposed to do. And it's also not doing what it's really supposed to do. It's not working for anyone.

So I say let's get rid of it. Rookies are free agents. They can negotiate with whatever teams they'd like and sign with the one that makes them the most attractive offer. Teams, likewise, can negotiate with and sign as many rookies as they can afford.

This seems like a radical idea, but I claim that the results won't look too much different than they do under the current system. Bad teams often have lots of cap room and would (and should) be willing to roll the dice on a young player or two with superstar potential. The good teams in general won't have as much money to burn and will likely settle for a less expensive rookies who plug specific holes. The teams that would lose out, compared to the draft system, are the ones that are bad but have no cap room. The winners are good teams with lots of cap space. That's OK with me. A bad team with no cap room is one that in my opinion doesn't deserve help.

If the results would be similar to what we see now, why do I favor a switch? Four reasons:

1. It's just a morally better system. This is cliche, but these 22-year-olds should be allowed to negotiate with several potential employers just as 22-year-olds in other careers get to. I don't mean to imply that rookies-to-be are being mistreated under the current system, but if it doesn't do any harm to anyone else (and it wouldn't), I do think it would be nice if they had the chance to explore various options like everyone else does.

2. It would end the ugly holdouts. Players wouldn't have a team to hold out from. No particular city would have a platoon of journalists riling up the fan base about how cheap management is. Players opting not to sign would be forgotten about pretty quickly.

3. It would create more diverse strategies with regard to acquiring young talent. Some teams would go for several big name players. Others would load up on guys that would formerly have been considered second or third round picks. More diverse strategies almost always make for a more interesting game.

The Rams have taken nine running backs in the first round; no other team has taken more than six. How many of those Ram runners can you name off the top of your head in under 30 seconds?

Two teams have drafted three tight ends in the first round: the Jets (Anthony Becht, Kyle Brady, and Johnny Mitchell) and Steelers (Heath Miller, Mark Breuner, and Eric Green). Twelve teams have never (since 1978) drafted a first-round tight end.

The Redskins have been allergic to the draft for far longer than Dan Snyder has been calling the shots. They have had the fewest first round picks (18) among all teams that have been in existence for the entire period. Denver (22) has the next fewest. The Bengals (36) have the most.

The Colts have drafted four first round quarterbacks. The first three were Art Schlichter, John Elway, and Jeff George. Ryan Leaf would have fit in well with this group.

Only two teams have never (since 1978) taken a first round quarterback. They are the Rams and Saints.

The team who has spent the greatest percentage of its first rounders on offense has been the Lions. The most historically defense oriented team in the first round has been the Cowboys, who have drafted more defensive linemen in the first round than offensive players combined.

It's interesting that the Steelers, a team generally known for good defenses, have spent far more of their first round picks on offense, while the 49ers have spent the majority of their picks on defense.

Just this weekend I decided to join the second half of the first decade of the millennium by learning how to put little tooltips on my web pages.

I have never been a fan of menus that expand into enormous submenus when you mouse over them. It seems like I'm always trying to click or read something under the real estate the enormous submenu will claim when I inadvertently drag my mouse across the menu item and the text or link I'm interested in gets clobbered.

On the other hand, I have seen sites make good use of small popup text bubbles that give you a quick bit of information when you mouse over some text, and then disappear when you drag the mouse away.

So I'm not sure if this is a good idea or not, and that's why I'm starting small. When you go to a p-f-r team page, like this one, and look at the team's results, mousing over the opponent will show you that opponent's record. Likewise, when you are at a player page and you mouse over the three-letter team abbreviation in his yearly stat line, it will show that team's record.

It seems to work in Firefox and IE, but apparently not so well in Safari. I suspect that's a minor setback that I can get it worked out. Obviously if I can't make it work in all browsers, then it won't become a part of the site.

Aside from that, what do you think? If you're for it, then how far should it go? What if instead of just the record, it was the record, the coach, the leading passer, rusher, and receiver, and the teams ranks in various categories? What if one could mouse over the "G" column and have the entire game log pop up, instead of having to click over to a completely separate page for the game logs? How much is too much?

A few readers remarked that the word "consistent" implies some sort of year-to-year consistency. I hadn't intended to measure that with the previous post but it's equally interesting to look at. A reader named Yaguar proposed the following methodology:

Now, what you measure is win difference over each 2 year period, and then average them. So take the 1999-2000 Colts, who regressed from 13-3 to 10-6. That’s a win difference of 3 for 1999-2000. (Note that you’re taking absolute value, so there can’t be negative changes in wins.) For 2000-2001 and 2001-2002, they have win differences of 4 both times, going from 10-6 to 6-10 to 10-6. So from 1999-2002, the Colts have an average win difference of 3.33.

The first number is the average win difference that Yaguar explained. The following string of numbers are the number of times the given team has had each given win difference. Take the Cardinals, for instance. Six times, their record stayed constant from one year to the next, seven times it changed by one game (one way or the other), five times it changed by two games, and so on.

As could be expected, there are some similarities between this list and the other one. The Cardinals show as the most consistent on both lists, and Miami, Seattle, and Minnesota are near the top on both as well, while the 49ers, Colts, and Rams look inconsistent either way.

The Cowboys are an interesting case, though. They rank as one of the least consistent franchises by the other method and one of the most by this one. This means that they've experienced some high highs and low lows, but that they have transitioned gradually between them. Denver represents the other side of the spectrum: a team whose win totals have generally stayed within a comparatively narrow band over a long period (24 of their last 29 seasons have been between 8 and 13 wins inclusive), but have jumped around a lot within that band from year to year.

I found an error in my calculations in Wednesday's post. Fortunately, the important conclusions remain essentially unchanged.

What happened was that, in the regressions I ran, each team was being included several times. So the data was essentially right, but the repetitions made the sample size bigger and therefore made one of the coefficients look significant when in fact it wasn't.

In Wednesday's post, I ran three regressions. I claimed that NFL pick value chart value was not statistically significant in any of them, and that Massey-Thaler draft value was significant in one of them. In actuality, neither variable was significant in any of the regressions.

So my conclusion does change a bit. Here is what it used to say:

Assuming the regression is technically OK, these results simultaneously validate Massey and Thaler’s paper and also my argument against it. More precisely, the data show that M-T value is a more relevant measure of draft value than pick value chart value is. But they also show that the distinction is nearly trivial.

It now says this:

Assuming the regression is technically OK, these results validate my criticism of the Massey-Thaler paper. Namely, teams do not appear to be able to the translate the theoretical surplus value they get from their draft picks into surplus production on the field. That's probably because the difference in theoretical average value between draft picks is so small that it's swamped by other factors. One of those factors, of course, is what the teams actually do with those picks. In other words, it's much, much less important for a team to know that pick #1 is on average less valuable than pick #30 than it is for them to know that Peyton Manning is better than Ryan Leaf (if they're picking #1) or that Chad Johnson is better than Quincy Morgan (if they're picking #30). What Massey and Thaler's paper shows is that the NFL draft is a meritocracy, or maybe a luckocracy, but it's not in its present form a mechanism for promoting parity.

[NOTE: this post was edited to correct an error a couple of days after its original posting. The error is explained here.]

This is a continuation of last Wednesday's and Friday's posts about Cade Massey and Richard Thaler's study of the NFL draft.

They claim to have shown that having the first draft slot is a disadvantage. I claim they've shown that all draft slots in the first three rounds are essentially of equal value. That's not because first round players aren't better than third round players --- they are, at least on average --- it's because first round, second round, and third round players will, on average, outperform their contract by roughly equal amounts. In a salary capped world, that makes those picks equally valuable.

But that's all theoretical. What I want to know is, does it translate to wins and losses? If, as Massey and Thaler claim, high first round picks are a liability compared to later first round picks and second round picks, then teams with lots of valuable (according to their study) picks should improve more quickly than similar teams without such picks.

This is a sticky question because so many factors are involved. For example, consider the following table, which consists of actual data:

"High" and "low" are defined by "above the median" and below the median." In other words, I looked at all teams that won 3 or fewer games in Year N-1 and sorted them by M-T value in the Year N draft. I cut the list in half and called the top half the High M-T Value group and the bottom half the Low Value group.

This would seem to indicate that M-T value does play some small role in team improvements during the three year period. But the problem is if you do the analogous breakdown by NFL pick value chart value, you'll get similar results. That's to be expected, because chart value and M-T value are positively associated. Teams that have a lot of picks generally have a lot of both kinds of value. In order to put the Massey-Thaler theory to the test, we need to separate the two.

The only way I know to do that is with regression. As I've mentioned before, regression is an unbelievably complex subject. Like most people, I don't fully understand all its intricacies. Also like most people, I'm going to go ahead and use it anyway. The only difference is I'm going to warn you that I'm not completely sure if what I've done is OK. So take it for what it's worth.

I ran a regression with the following input variables:

Team record in year N-1

Total Massey-Thaler draft value in the Year N draft (described in Friday's post), in millions of dollars of surplus value

Total NFL draft pick value chart value in the Year N draft (also described in the above-linked post) in their usual units. The first pick is 3000, the 2nd pick is 2600, and so on down to the last pick, which is worth essentially zero.

Again, neither coefficient is significant. Even if they were statistically significant, they're small enough that it's clear that they have no practical significance, as the following thought experiment shows.

Suppose the Raiders swapped their #1 overall pick straight up for the Colts' #32 overall pick. In giving up #1 and getting back #32, the Raiders gain a net of about .13 million in Massey-Thaler value. Multiplying .13 by the appropriate coefficient (.32) yields about .01 wins. In a three year period.

The R^2 of this regression was about .07 which means that if you want to predict an NFL team's wins during the period 2007--2009 using its 2006 record and the M-T and NFL values of its 2007 draft picks, you're not going to be very successful. But that's pretty obvious.

Assuming the regression is technically OK, these results validate my criticism of the Massey-Thaler paper. Namely, teams do not appear to be able to the translate the theoretical surplus value they get from their draft picks into surplus production on the field. That's probably because the difference in theoretical average value between draft picks is so small that it's swamped by other factors. One of those factors, of course, is what the teams actually do with those picks. In other words, it's much, much less important for a team to know that pick #1 is on average less valuable than pick #30 than it is for them to know that Peyton Manning is better than Ryan Leaf (if they're picking #1) or that Chad Johnson is better than Quincy Morgan (if they're picking #30). What Massey and Thaler's paper shows is that the NFL draft is a meritocracy, or maybe a luckocracy, but it's not in its present form a mechanism for promoting parity.

My good friend John-Charles Bradbury has written a book called The Baseball Economist, which just hit the shelves a few weeks ago. There are a couple of reasons why I can't call this post a review of the book, or at least not an objective review: (1) as I've already admitted, the author is a friend, and (2) some of my own work is included.

Most of you are probably not aware that I used to be as intensely into baseball analysis as I currently am into football. I wrote for a few sabermetric sites and publications and I like to think I came up with a few nifty little studies along the way and contributed a bit to the field. But it's now clear that my biggest contribution (by far) was that I introduced John-Charles Bradbury to the existence of sabermetrics.

I could drone on about how much of a hero I am for leading J.C. out of the wilderness of RBIs and pitchers' wins, but I'll spare you. It is worth mentioning, though, that the fact that J.C. didn't encounter sabermetrics until relatively late in life probably prevented him from becoming Just Another Sabermetrician. Rather than viewing things through a traditional sabermetric lens --- as those of us who grew up with Bill James tend to do --- he started to look at them in light of his training as a professional economist. When combined with the tools of sabermetrics, it leads to a fresh perspective.

If you're turned off by "the business of baseball," don't let the title of the book scare you. While it does contain a few chapters about issues traditionally associated with economics --- salaries, the reserve clause, the anti-trust exemption, and so forth --- it's not just about the economics of the game; it's also about the economics in the game.

What does that mean exactly? It means that economics isn't about money. The best-selling book Freakonomics has made the general public aware that there is virtually no topic into which economists won't stick their noses (including the fourth-down decisions of NFL coaches and draft day trades in the NFL). Economics isn't about GDPs and discount rates and money multipliers; it's a framework for studying human behavior. Since baseball players (and managers, and owners, and umpires, and fans) are human beings, economic theories often attempt to predict how they will behave in certain situations.

If you're like me, you like to read books that introduce you to the core concepts of different disciplines. But you're not willing to work too hard. I don't want a PhD in economics (or psychology, or linguistics, or whatever), I just want a brief introduction to the general mode of thought. J.C. provides this in a clear and easy-to-read way. But, while this book is easy to read, don't get the idea that it's trivial. Economists and hard core sabermetricians will undoubtedly read a few things that are not news to them, but everyone will find plenty of new ideas in this book. I know I did, despite the fact that I ate lunch with J.C. every Friday during the entire time he was writing it!

The Baseball Economist does a very nice job of clearly explaining various economic theories and concepts and examining how they play out on the baseball diamond and in the front office. If you're not an economist, you probably won't agree with all his conclusions, or even his methods, but if you have an analytical mind, his arguments will make you think.